Conduction Velocity Restitution Research Articles

Alternans Resonance and Propagation Block during Supernormal Conduction in Cardiac Tissue with Decreased [K+

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K+]o. In control [K+]o simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.

Asymptotics of Conduction Velocity Restitution in Models of Electrical Excitation in the Heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh-Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified "caricature" of Noble (J. Physiol. Lond. 160:317-352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177-210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler-Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.

Structural Heterogeneity Alone Is a Sufficient Substrate for Dynamic Instability and Altered Restitution

Marked changes in ventricular APD restitution and associated alternans rhythm have been demonstrated in structural heart disease (SHD). However, whether this is due to structural heterogeneity or regional variation in cellular properties remains uncertain. In this study, we address the hypothesis that the structural heterogeneity associated with SHD is sufficient to alter dynamic restitution and increase the probability of electric instability. Activation was simulated in a 14x14 mm(2) domain in the presence and absence (control) of a central region containing nonuniform discontinuities resembling patchy fibrosis. A modified LR1 cardiac activation model was used in a bidomain formulation with isotropic conductivities. Bipolar stimulation was imposed above the central region with coupling intervals decreasing progressively from 500 ms and then maintained at 105 ms. Structural discontinuities had little effect on electric activation at low stimulus rates, but activation time and APD distributions became highly nonuniform within and adjacent to the discontinuous region at high rates. Discordant APD alternans occurred in both "fibrosis" and control, but at lower stimulus rates and with markedly greater extent in the former. Tortuous conduction through the discontinuous region resulted in large fluctuations of diastolic intervals giving rise to regional electric instability, which modulates dynamic conduction velocity and APD restitution. This led to heterogeneous conduction block and reentry not observed in control. We show that structural discontinuities can amplify discordant alternans and provide a rate-dependent substrate for reentry. This work provides new insights into the mechanisms by which fibrosis may contribute to arrhythmogenesis.

The dynamic nature of ventricular tachycardia initiation

Initiation of ventricular tachycardia (VT) or ventricular fibrillation (VF) requires heterogeneity of the substrate. This heterogeneity has a stable/fixed component (structural or functional) and a dynamic component. The latter explains the random and sudden destabilization of the substrate and the initiation of VT or VF by a ventricular extra stimulus trigger. The main mechanisms of dynamic heterogeneity are discussed at the cellular level (action potential duration alternans and restitution and intracellular calcium cycling instability) and at the tissue level (conduction velocity restitution and concordant and discordant alternans). Better knowledge of dynamic factors in arrhythmogenesis has an overwhelming impact on both predicting malignant arrhythmias and changing the antiarrhythmic drug paradigm from suppressing triggers to modifying dynamic instability factors.

Evidence of a Pro-Arrhythmic Substrate in the Failing Right Ventricle of Pulmonary Hypertensive Rats

Arrhythmic risk is increased in patients with heart failure. We have investigated the arrhythmic state of the failing right ventricle in a model of pulmonary hypertension (PAH).Wistar rats were injected intraperitoneally with monocrotaline (MCT, 60 mg/kg) to induce PAH and right ventricular failure within 3-4 weeks and compared to age-matched saline-injected animals (CON).In vivo measurement of ECG parameters using radiotelemetry indicated modification of T wave-parameters in MCT treated animals e.g. a prolonged QT interval (CON 49.7±2.0 vs. MCT 76.2±2.5 ms, P<0.001) and time from the peak to the end of the T-wave (Tpe, CON 25±1.8 vs. MCT 33.1±1.7 ms, P = 0.007) (CON n = 6, MCT n = 7).Animals were humanely killed upon showing clinical symptoms of HF. Monophasic action potentials (MAPs) were recorded at the right ventricular epicardial surface of isolated hearts and a S1-S2 protocol used to construct standard APD restitution curves. MAP duration was significantly prolonged in failing hearts (MAP90, 39.9±1.9 ms in CON vs. 80.7±3.5 ms in MCT, P<0.001) and standard restitution slopes were steeper (mean maximum slope was 0.18±0.02 CON vs. 0.73±0.28 MCT, P<0.001).Optical action potentials were recorded at stimulation frequencies between 5-12 Hz using the voltage-sensitive dye di-4-ANEPPS and dynamic APD and conduction velocity restitution curves measured. The failing right ventricle exhibited steeper restitution and conduction velocity restitution curves (mean maximum slope for conduction velocity was 0.013±0.004 MCT vs. 0.002±0.001 CON, P<0.001). At high pacing frequencies, arrhythmias were induced in failing but not in control hearts.T-wave modification, APD prolongation, steeper APD and conduction velocity restitution curves are typically associated with a pro-arrhythmic state. We conclude that the failing right ventricle of pulmonary hypertensive rats have an elevated risk of developing arrhythmias. The underlying mechanisms are under investigation.

Origin of complex behaviour of spatially discordant alternans in a transgenic rabbit model of type 2 long QT syndrome

Enhanced dispersion of repolarization has been proposed as an important mechanism in long QT related arrhythmias. Dispersion can be dynamic and can be augmented with the occurrence of spatially out-of-phase action potential duration (APD) alternans (discordant alternans; DA). We investigated the role of tissue heterogeneity in generating DA using a novel transgenic rabbit model of type 2 long QT syndrome (LQT2). Littermate control (LMC) and LQT2 rabbit hearts (n = 5 for each) were retrogradely perfused and action potentials were mapped from the epicardial surface using di-4-ANEPPS and a high speed CMOS camera. Spatial dispersion (Delta APD and Delta slope of APD restitution) were both increased in LQT2 compared to LMC (Delta APD: 34 +/- 7 ms vs. 23 +/- 6 ms; Delta slope: 1.14 +/- 0.23 vs. 0.59 +/- 0.19). Onset of DA under a ramp stimulation protocol was seen at longer pacing cycle length (CL) in LQT2 compared to LMC hearts (206 +/- 24 ms vs. 156 +/- 5 ms). Nodal lines between regions with APD alternans out of phase from each other were correlated with conduction velocity (CV) alternation in LMC but not in LQT2 hearts. In LQT2 hearts, larger APD dispersion was associated with onset of DA at longer pacing CL. At shorter CLs, closer to ventricular fibrillation induction (VF), nodal lines in LQT2 (n = 2 out of 5) showed persistent complex beat-to-beat changes in nodal line formation of DA associated with competing contribution from CV restitution and tissue spatial heterogeneity, increasing vulnerability to conduction block. In conclusion, tissue heterogeneity plays a significant role in providing substrate for ventricular arrhythmia in LQT2 rabbits by facilitating DA onset and contributing to unstable nodal lines prone to reentry formation.

Cardiac alternans induced by fibroblast-myocyte coupling: mechanistic insights from computational models

Recent experimental studies have shown that fibroblasts can electrotonically couple to myocytes via gap junctions. In this study, we investigated how this coupling affects action potential and intracellular calcium (Ca(i)) cycling dynamics in simulated fibroblast-myocyte pairs and in two-dimensional tissue with random fibroblast insertions. We show that a fibroblast coupled with a myocyte generates a gap junction current flowing to the myocyte with two main components: an early pulse of transient outward current, similar to the fast transient outward current, and a later background current during the repolarizing phase. Depending on the relative prominence of the two components, fibroblast-myoycte coupling can 1) prolong or shorten action potential duration (APD), 2) promote or suppress APD alternans due to steep APD restitution (voltage driven) and also result in a novel mechanism of APD alternans at slow heart rates, 3) promote Ca(i)-driven alternans and electromechanically discordant alternans, and 4) promote spatially discordant alternans by two mechanisms: by altering conduction velocity restitution and by heterogeneous fibroblast distribution causing electromechanically concordant and discordant alternans in different regions of the tissue. Thus, through their coupling with myocytes, fibroblasts alter repolarization and Ca(i) cycling alternans at both the cellular and tissue scales, which may play important roles in arrhythmogenesis in diseased cardiac tissue with fibrosis.

Therapeutic Hypothermia (30.DEG.C) Enhances Arrhythmogenic Substrates, Including Spatially Discordant Alternans, and Facilitates Pacing-Induced Ventricular Fibrillation in Isolated Rabbit Hearts

Therapeutic hypothermia (TH, 30 degrees C) protects the brain from hypoxic injury. However, TH may potentiate the occurrence of lethal ventricular fibrillation (VF), although the mechanism remains unclear. The present study explored the hypothesis that TH enhances wavebreaks during VF and S(1) pacing, facilitates pacing-induced spatially discordant alternans (SDA), and increases the vulnerability of pacing-induced VF. Using an optical mapping system, epicardial activations of VF were studied in 7 Langendorff-perfused isolated rabbit hearts at baseline (37 degrees C), TH (30 degrees C), and rewarming (37 degrees C). Action potential duration (APD)/conduction velocity (CV) restitution and APD alternans (n=6 hearts) were determined by S(1) pacing at these 3 stages. During TH, there was a higher percentage of VF duration containing epicardial repetitive activities (spatiotemporal periodicity) (P<0.001). However, TH increased phase singularity number (wavebreaks) during VF (P<0.05) and S(1) pacing (P<0.05). TH resulted in earlier onset of APD alternans (P<0.001), which was predominantly SDA (P<0.05), and increased pacing-induced VF episodes (P<0.05). TH also decreased CV, shortened wavelength, and enhanced APD dispersion and the spatial heterogeneity of CV restitution. TH (30 degrees C) increased the vulnerability of pacing-induced VF by (1)facilitating wavebreaks during VF and S(1) pacing, and (2)enhancing proarrhythmic electrophysiological parameters, including promoting earlier onset of APD alternans (predominantly SDA) during S(1) pacing.

The Transfer Functions of Cardiac Tissue during Stochastic Pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K +]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.

Slow and Discontinuous Conduction Conspire in Brugada Syndrome

Brugada syndrome (BrS) is associated with lethal arrhythmias, which are linked to specific ST-segment changes (type-1 BrS-ECG) and the right ventricle (RV). The pathophysiological basis of the arrhythmias and type-1 BrS-ECG is unresolved. We studied the electrophysiological characteristics of the RV endocardium in BrS. RV endocardial electroanatomical mapping and stimulation studies were performed in controls (n=12) and BrS patients with a type-1 (BrS-1, n=10) or type-2 BrS-ECG (BrS-2, n=12) during the studies. BrS-1 patients had prominent impairment of RV endocardial impulse propagation when compared with controls, as represented by: (1) prolonged activation-duration during sinus rhythm (86+/-4 versus 65+/-3 ms), (2) increased electrogram fractionation (1.36+/-0.04 versus 1.15+/-0.01 deflections per electrogram), (3) longer electrogram duration (83+/-3 versus 63+/-2 ms), (4) activation delays on premature stimulation (longitudinal: 160+/-26 versus 86+/-9 ms; transversal: 112+/-5 versus 58+/-6 ms), and (5) abnormal transversal conduction velocity restitution (42+/-8 versus 18+/-2 ms increase in delay at shortest coupling intervals). Wider and more fractionated electrograms were also found in BrS-2 patients. Repolarization was not different between groups. BrS-1 and BrS-2 patients are characterized by wide and fractionated electrograms at the RV endocardium. BrS-1 patients display additional conduction slowing during sinus rhythm and premature stimulation along with abnormal transversal conduction velocity restitution. These patients may thus exhibit a substrate for slow and discontinuous conduction caused by abnormal active membrane processes and electric coupling. Our findings support the emerging notion that BrS is not solely attributable to abnormal electrophysiological properties but requires the conspiring effects of conduction slowing and tissue discontinuities.

Atrial proarrhythmia due to increased inward rectifier current (IK1) arising from KCNJ2 mutation – A simulation study

Atrial fibrillation (AF) has been linked to increased inward rectifier potassium current, IK1, either due to AF-induced electrical remodelling, or from functional changes due to the Kir2.1 V93I mutation. The aim of this simulation study was to identify at cell and tissue levels' mechanisms by which increased IK1 facilitates and perpetuates AF. The Courtemanche et al. human atrial cell action potential (AP) model was modified to incorporate reported changes in IK1 induced by the Kir2.1 V93I mutation in both heterozygous (Het) and homozygous (Hom) mutant forms. The modified models for wild type (WT), Het and Hom conditions were incorporated into homogeneous 1D, 2D and 3D tissue models. Restitution curves of AP duration (APD), effective refractory period (ERP) and conduction velocity (CV) were computed and both the temporal and the spatial vulnerability of atrial tissue to re-entry were measured. The lifespan and tip meandering pattern of re-entry were also characterised. For comparison, parallel simulations were performed by incorporating into the Courtmanche et al. model a linear increase in maximal IK1 conductance. It was found that the gain-in-function of V93I ‘mutant’IK1 led to abbreviated atrial APs and flattened APD, ERP and CV restitution curves. It also hyperpolarised atrial resting membrane potential and slowed down intra-atrial conduction. V93I ‘mutant’IK1 reduced the tissue's temporal vulnerability but increased spatial vulnerability to initiate and sustain re-entry, resulting in an increased overall susceptibility of atrial tissue to arrhythmogenesis. In the 2D model, spiral waves self-terminated for WT (lifespan < 3.3 s) tissue, but persisted in Het and Hom tissues for the whole simulation period (lifespan > 10 s). The tip of the spiral wave meandered more in WT tissue than in Het and Hom tissues. Increased IK1 due to augmented maximal conductance produced similar results to those of Het and Hom Kir2.1 V93I mutant conditions. In the 3D model the dynamic behaviour of scroll waves was stabilized by increased IK1. In conclusion, increased IK1 current, either by the Kir2.1 V93I mutation or by augmented maximal conductance, increases atrial susceptibility to arrhythmia by increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue, thereby facilitating initiation and maintenance of re-entrant circuits.

Properties of two human atrial cell models in tissue: Restitution, memory, propagation, and reentry

To date, two detailed ionic models of human atrial cell electrophysiology have been developed, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models draw from similar experimental data, they have vastly different properties. This paper provides the first systematic analysis and comparison of the dynamics of these models in spatially extended systems including one-dimensional cables and rings, two-dimensional sheets, and a realistic three-dimensional human atrial geometry. We observe that, as in single cells, the CM adapts to rate changes primarily by changes in action potential duration (APD) and morphology, while for the NM rate changes affect resting membrane potential (RMP) more than APD. The models also exhibit different memory properties as assessed through S1–S2 APD and conduction velocity (CV) restitution curves with different S1 cycle lengths. Reentrant wave dynamics also differ, with the NM exhibiting stable, non-breaking spirals and the CM exhibiting frequent transient wave breaks. The realistic atrial geometry modifies dynamics in some cases through drift, transient pinning, and breakup. Previously proposed modifications to represent atrial fibrillation-remodeled electrophysiology produce altered dynamics, including reduced rate adaptation and memory for both models and conversion to stable reentry for the CM. Furthermore, proposed variations to the NM to reproduce action potentials more closely resembling those of the CM do not substantially alter the underlying dynamics of the model, so that tissue simulations using these modifications still behave more like the unmodified NM. Finally, interchanging the transmembrane current formulations of the two models suggests that currents contribute more strongly to RMP and CV, intracellular calcium dynamics primarily determine reentrant wave dynamics, and both are important in APD restitution and memory in these models. This finding implies that the formulation of intracellular calcium processes is as important to producing realistic models as transmembrane currents.

Role of Conduction Velocity Restitution and Short-Term Memory in the Development of Action Potential Duration Alternans in Isolated Rabbit Hearts

Spatially discordant alternans (SDA) has been linked to life-threatening arrhythmias. The mechanisms underlying SDA development in cardiac tissue remain unclear. We investigated the role of conduction velocity (CV) restitution and short-term memory in the organization and evolution of alternans in action potential duration using high-resolution optical mapping of the epicardial surface in 8 isolated, Langendorff-perfused rabbit hearts. To assess the spatial organization of alternans, we tracked the evolution of nodal lines that separate out-of-phase regions of SDA. We measured the action potential duration heterogeneity index and maximal slope of CV restitution and estimated the effects of short-term memory by calculating time constant of action potential duration accommodation (tau). We found that 2 mechanisms underlie the development of SDA in the heart, leading to 2 distinct behaviors of nodal lines. The first mechanism is based on steep CV restitution and is associated with small tau and stable nodal lines. The second mechanism is associated with short-term memory (large tau) and is characterized by shallow CV restitution and unstable behavior of nodal lines. The maximum slope of the CV restitution was steeper (18.16+/-3.34 m/s(2)) and tau was smaller (tau=4.31+/-0.33 stimuli) for areas with stable nodal lines than for areas with unstable nodal lines (6.32+/-0.96 m/s(2) and tau=10.3+/-1.84 stimuli; P<0.01). Our results provide new insight into the mechanisms underlying SDA formation in the rabbit heart. Specifically, our results suggest that a new mechanism associated with short-term memory underlies SDA formation in the heart, in addition to steep CV restitution.

Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher–Noble–Noble–Panfilov (TNNP), and the Iyer–Mazhari–Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.

Spatially discordant alternans in cardiomyocyte monolayers

Repolarization alternans is a harbinger of sudden cardiac death, particularly when it becomes spatially discordant. Alternans, a beat-to-beat alternation in the action potential duration (APD) and intracellular Ca (Cai), can arise from either tissue heterogeneities or dynamic factors. Distinguishing between these mechanisms in normal cardiac tissue is difficult because of inherent complex three-dimensional tissue heterogeneities. To evaluate repolarization alternans in a simpler two-dimensional cardiac substrate, we optically recorded voltage and/or Cai in monolayers of cultured neonatal rat ventricular myocytes during rapid pacing, before and after exposure to BAY K 8644 to enhance dynamic factors promoting alternans. Under control conditions (n = 37), rapid pacing caused detectable APD alternans in 81% of monolayers, and Cai transient alternans in all monolayers, becoming spatially discordant in 62%. After BAY K 8644 (n = 28), conduction velocity restitution became more prominent, and APD and Cai alternans developed and became spatially discordant in all monolayers, with an increased number of nodal lines separating out-of-phase alternating regions. Nodal lines moved closer to the pacing site with faster pacing rates and changed orientation when the pacing site was moved, as predicted for the dynamically generated, but not heterogeneity-based, alternans. Spatial APD gradients during spatially discordant alternans were sufficiently steep to induce conduction block and reentry. These findings indicate that spatially discordant alternans severe enough to initiate reentry can be readily induced by pacing in two-dimensional cardiac tissue and behaves according to predictions for a predominantly dynamically generated mechanism.

Analysis of Damped Oscillations during Reentry: A New Approach to Evaluate Cardiac Restitution

Reentry is a mechanism underlying numerous cardiac arrhythmias. During reentry, head-tail interactions of the action potential can cause cycle length (CL) oscillations and affect the stability of reentry. We developed a method based on a difference-delay equation to determine the slopes of the action potential duration and conduction velocity restitution functions, known to be major determinants of reentrant arrhythmogenesis, from the spatial period P and the decay length D of damped CL oscillations. Using this approach, we analyzed CL oscillations after the induction of reentry and the resetting of reentry with electrical stimuli in rings of cultured neonatal rat ventricular myocytes grown on microelectrode arrays and in corresponding simulations with the Luo-Rudy model. In the experiments, P was larger and D was smaller after resetting impulses compared to the induction of reentry, indicating that reentry became more stable. Both restitution slopes were smaller. Consistent with the experimental findings, resetting of simulated reentry caused oscillations with gradually increasing P, decreasing D, and decreasing restitution slopes. However, these parameters remained constant when ion concentrations were clamped, revealing that intracellular ion accumulation stabilizes reentry. Thus, the analysis of CL oscillations during reentry opens new perspectives to gain quantitative insight into action potential restitution.

Vulnerability to re-entry in simulated two-dimensional cardiac tissue: Effects of electrical restitution and stimulation sequence

Ventricular fibrillation is a lethal arrhythmia characterized by multiple wavelets usually starting from a single or figure-of-eight re-entrant circuit. Understanding the factors regulating vulnerability to the re-entry is essential for developing effective therapeutic strategies to prevent ventricular fibrillation. In this study, we investigated how pre-existing tissue heterogeneities and electrical restitution properties affect the initiation of re-entry by premature extrastimuli in two-dimensional cardiac tissue models. We studied two pacing protocols for inducing re-entry following the "sinus" rhythm (S1) beat: (1) a single premature (S2) extrastimulus in heterogeneous tissue; (2) two premature extrastimuli (S2 and S3) in homogeneous tissue. In the first case, the vulnerable window of re-entry is determined by the spatial dimension and extent of the heterogeneity, and is also affected by electrical restitution properties and the location of the premature stimulus. The vulnerable window first increases as the action potential duration (APD) difference between the inside and outside of the heterogeneous region increases, but then decreases as this difference increases further. Steeper APD restitution reduces the vulnerable window of re-entry. In the second case, electrical restitution plays an essential role. When APD restitution is flat, no re-entry can be induced. When APD restitution is steep, re-entry can be induced by an S3 over a range of S1S2 intervals, which is also affected by conduction velocity restitution. When APD restitution is even steeper, the vulnerable window is reduced due to collision of the spiral tips.

Mechanisms of arrythmogenic cardiac alternans

T-wave alternans, a powerful marker for the risk of sudden cardiac death is directly related to alternans of the cellular action potential. When action potential alternans is first initiated, it occurs with identical phase in all cells of a particular region of the heart. However, above a critical heart rate threshold, action potential alternans switches phase in some cells but not in others, such that some cells undergo a prolongation of action potential duration (APD), whereas neighbouring cells undergo APD shortening on the same beat (i.e. discordant alternans). Discordant alternans is linked to a mechanism of arrhythmogenesis because when ventricular action potentials from neighbouring cells are alternating out of phase, repolarization gradients are amplified, producing conduction block and re-entrant excitation. In this review, we discuss potential mechanisms which may underlie discordant alternans in the heart, including (i) conduction velocity restitution, (ii) spatial heterogeneities of calcium cycling and the sarcolemmal ionic currents which govern repolarization, and (iii) intercellular uncoupling.

The Role of Cardiac Tissue Alignment in Modulating Electrical Function

Most cardiac arrhythmias are associated with pathology-triggered ion channel remodeling. However, multicellular effects, for example, exaggerated anisotropy and altered cell-to-cell coupling, can also indirectly affect action potential morphology and electrical stability via changed electrotonus. These changes are particularly relevant in structural heart disease, including hypertrophy and infarction. Recent computational studies showed that electrotonus factors into stability by altering dynamic properties (restitution). We experimentally address the question of how cell alignment and connectivity alter tissue function and whether these effects depend on the direction of wave propagation. We show that cardiac cell arrangement can alter electrical stability in an in vitro cardiac tissue model by mechanisms both dependent and independent of the direction of wave propagation, and local structural remodeling can be felt beyond a space constant. Notably, restitution of action potential duration (APD) and conduction velocity was significantly steepened in the direction of cell alignment. Furthermore, prolongation of APD and calcium transient duration was found in highly anisotropic cell networks, both for longitudinal and transverse propagation. This is in contrast to expected correlation between wave propagation direction and APD based on electrotonic effects only, but is consistent with our findings of increased cell size and secretion of atrial natriuretic factor, a hypertrophy marker, in the aligned structures. Our results show that anisotropic structure is a potent modulator of electrical stability via electrotonus and molecular signaling. Tissue alignment must be taken into account in experimental and computational models of arrhythmia generation and in designing effective treatment therapies.

Vulnerable Window for Conduction Block in a One-Dimensional Cable of Cardiac Cells, 1: Single Extrasystoles

Spatial dispersion of refractoriness, which is amplified by genetic diseases, drugs, and electrical and structural remodeling during heart disease, is recognized as a major factor increasing the risk of lethal arrhythmias and sudden cardiac death. Dispersion forms the substrate for unidirectional conduction block, which is required for the initiation of reentry by extrasystoles or rapid pacing. In this study, we examine theoretically and numerically how preexisting gradients in refractoriness control the vulnerable window for unidirectional conduction block by a single premature extrasystole. Using a kinematic model to represent wavefront-waveback interactions, we first analytically derived the relationship (under simplified conditions) between the vulnerable window and various electrophysiological parameters such as action potential duration gradients, refractoriness barriers, conduction velocity restitution, etc. We then compared these findings to numerical simulations using the kinematic model or the Luo-Rudy action potential model in a one-dimensional cable of cardiac cells. The results from all three methods agreed well. We show that a critical gradient in action potential duration for conduction block can be analytically derived, and once this critical gradient is exceeded, the vulnerable window increases proportionately with the refractory barrier and is modulated by conduction velocity restitution and gap junctional conductance. Moreover, the critical gradient for conduction block is higher for an extrasystole traveling in the opposite direction from the sinus beat than for one traveling in the same direction (e.g., an epicardial extrasystole versus an endocardial extrasystole).